Application of the Lagrange-Charpit method to analyse the power system's stability

Abstract A systematic procedure for constructing Lyapunov functions is considered. The linear partial differential equation is written using the system equation and the arbitrary non-negative function φ.The Lyapunov function is obtained by integrating the partial differential equation, using the Lagrango-Charriit method. Then, the arbitrary function φ is handled from the integrable standpoint of the characteristic equation of the partial differential equation. The Lyapunov function obtained is used to describe the region of stability. The superiority of this method is illustrated by applying it to a single-machine system, which includes the damping effect, comparing the results with those obtained by conventional methods.